A082555 Primes whose base-3 representation does not contain a 0.

2, 5, 7, 13, 17, 23, 41, 43, 53, 67, 71, 79, 131, 149, 151, 157, 211, 229, 233, 239, 241, 367, 373, 401, 449, 457, 607, 617, 619, 643, 647, 691, 701, 719, 727, 1093, 1097, 1103, 1123, 1129, 1187, 1201, 1213, 1367, 1373, 1427, 1429, 1447, 1453, 1823, 1831, 1861

Offset: 1

Author

Randy L. Ekl, May 03 2003

Keywords

• base
• nonn

Comments

Primes in A032924. - Robert Israel, Dec 28 2018

The analog "primes without digit 2 in ternary" is A077717. There is no prime > 2 not having the digit 1 in ternary, since then the number is divisible by 2. - M. F. Hasler, Feb 15 2023

Examples

			41 = 1112_3, which contains no 0.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032924 (numbers without digit 0 in base 3), A073779, A077267.

Cf. A077717 (primes that are the sum of distinct powers of 3 <=> base-3 representation does not contain a digit 2).

Programs

Maple

select(t -> isprime(t) and not(has(convert(t,base,3),0)), [2,seq(i,i=5..10000,2)]); # Robert Israel, Dec 28 2018

PARI

dec3(s)=while(s>0,if(s%3==0,return(0),s=floor(s/3))); return(1)
forprime(i=1,20000,if(dec3(i)==1,print1(i,", "),))

Python

def is_A082555(n): return is_A032924(n) and A010051(n)
[p for p in range(1888) if is_A082555(p)] # M. F. Hasler, Feb 15 2023